This can be viewed as a generalized version of RT formula, which suggests that the extremal surfaces in any bulk regions have definite physical meanings. As a result, in the surface/state correspondence, there is a general rule for the extremal surfaces as follows [1]}: The density matrix corresponding to an extremal surface is a direct product of density matrices at each point, which means that the von Neumann entropy of the density matrix of an extremal surface is equal to its area (or in the language of tensor networks, it is just proportional to the number of bonds passing through the surface ).
